I find this intriguing. I think because I considered diving for literally decades, and hence walked into many dive shops over the years and asked, 'How does this work?', I still understood PADI from how it "used to be".
So when I got my certifications I walked into a (the now only) dive shop in my city. They handed me a zipper bag with a book and some other materials and said, "Read ALL of this, fill in ALL of the questions, including the extra page of dive planning calculations that we printed out. Then sign in with the email you gave us to the PADI website and watch ALL of the videos. When you've done that call us back and schedule for a Friday, Saturday and possibly Sunday of classroom + pool classes. After you pass that we'll take you out to a lake to do part 2."
So that is what I did.
Nitrox and Advanced were essentially the same. I paid, got a physical packet with books and other materials and an afternoon in a classroom for Nitrox, a weekend at a lake for Advanced Open Water.
From time to time I got weird ads from PADI about "eLearning", but I thought they were just trying to sell me the videos that I already paid for via the dive shop. I wasn't sure why they did this.
Now I'm realizing that I maybe could have gone direct to PADI, paid for something online, and that might have covered what was in the zipper pockets?
I would definitely feel less prepared if that is what I had done, but I'm "old" and being forced to read a physical book and fill out questions made me feel like I was learning stuff.
I don't know if my dive shop is doing things "old school" or if PADI is just trying to market more stuff direct on the Internet now, but I can see why people are a bit confused about PADI certifications if they are letting you sign up for and cover the book learning part via something online instead of walking into a shop and getting a physical packet along with a thorough explanation of how the process works.
It seems a lot like the confusion around your "card", where much information says you get only an "e-card" and other information says you are mailed a physical card, and in the end I was mailed physical cards. Meanwhile if I do log into the app it literally lists all of my certifications as "Certifications without an e-card" which to me, basically proves I'm certified on its own, so why do I need an "e-card"?
Basically more confusion based on PADI not doing a great job of being clear online about how things work. Possibly out of a profit motive, but possibly just because their independent certification dive shops and instructors are all free to do things differently?
P.S. I went to the PADI website and sure enough, they are selling the Open Water Diver course as an eLearning course. It seems odd to me to sell something like that to someone who isn't even sure that a dive shop exists for them to go finish at?
I guess this maybe makes sense if you are trying to get certified in an area that has no dive shop and want to do Open Water Part 1 (pool/confined water) at a remote location?
I still think PADI should basically direct people to a dive shop first, rather than letting people just click on and buy an online "class" for over $200 with very little explanation of what the process is.
Long text short: Many people here are saying the "correct" or "normal" path is to talk to a person at a dive shop first, but clearly PADI is not guiding people in that direction, so it isn't the "normal" anymore, and people finding PADI's website online won't be doing it that way.